Theorem bj-dfbi6

Description: Alternate definition of the biconditional. (Contributed by BJ, 4-Oct-2019)

	Ref	Expression
Assertion	bj-dfbi6	|- ( ( ph <-> ps ) <-> ( ( ph \/ ps ) <-> ( ph /\ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		bj-dfbi5	|- ( ( ph <-> ps ) <-> ( ( ph \/ ps ) -> ( ph /\ ps ) ) )
2		id	|- ( ( ( ph \/ ps ) -> ( ph /\ ps ) ) -> ( ( ph \/ ps ) -> ( ph /\ ps ) ) )
3		animorr	|- ( ( ph /\ ps ) -> ( ph \/ ps ) )
4	2 3	impbid1	|- ( ( ( ph \/ ps ) -> ( ph /\ ps ) ) -> ( ( ph \/ ps ) <-> ( ph /\ ps ) ) )
5		biimp	|- ( ( ( ph \/ ps ) <-> ( ph /\ ps ) ) -> ( ( ph \/ ps ) -> ( ph /\ ps ) ) )
6	4 5	impbii	|- ( ( ( ph \/ ps ) -> ( ph /\ ps ) ) <-> ( ( ph \/ ps ) <-> ( ph /\ ps ) ) )
7	1 6	bitri	|- ( ( ph <-> ps ) <-> ( ( ph \/ ps ) <-> ( ph /\ ps ) ) )